6.5 Graphing Linear Inequalities

Graphing Linear Equations A linear equation can be written in either ________________ Or in_____________ To graph we find the y-intercept then apply the slope

Graphing Inequalities Inequalities are graphed by figuring where the solution starts and using an arrow to indicate the solution region -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4

Linear Inequalities Equations The solutions to a linear equation are the ordered pairs (x,y) which make the equation… _______ The point ( 1, 2) ___________________ Inequalities So The solutions to a linear inequality are the ordered pairs (x,y) which make the inequality… _______

Solutions to Linear Inequalities Which ordered pairs make the inequality true? ______ ____________________________________________________________ But what about points like… ____, _____, ______, ____, ____

Solutions to Linear Inequalities (cont.) We can replace the points that form the boundary line with a _________________ And we can replace all of the points in the region above the line with a ________________ The graph of the line with a shaded region represents the graphical solution to the linear inequality above.

Graphing < or > Inequalities If we have an inequality with a > or < symbol we have to adjust the graph Just like on the number line if we want to indicate that the solution gets as close as possible but does not include a point we use an ________ Since we are using a line instead of a point to represent the boundary we use a ________________ The shaded region remains the same

Which Side to Shade? Graph the line which represents the boundary of the inequality Pick a __________to insert into the equation (usually ______________ if it is not on the line) If the point makes the inequality ________shade the side which ___________ the point If the points makes the inequality ___________ then shade the side that does not_________________ In this case Is _____ so shade the side _____________________

Graph the Linear Inequalities Pick ______as the test point __________________________

Graph the Linear Inequalities _____________________________

Graph the Linear Inequalities ______________________________